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Preprints, Working Papers, ... Year : 2021

Fragmentations with self-similar branching speeds

Abstract

We consider fragmentation processes with values in the space of marked partitions of N, i.e. partitions where each block is decorated with a nonnegative real number. Assuming that the marks on distinct blocks evolve as independent positive self-similar Markov processes and determine the speed at which their blocks fragment, we get a natural generalization of the self-similar fragmentations of Bertoin (2002). Our main result is the characterization of these generalized fragmentation processes: a Lévy-Khinchin representation is obtained, using techniques from positive self-similar Markov processes and from classical fragmentation processes. We then give sufficient conditions for their absorption in finite time to a frozen state, and for the genealogical tree of the process to have finite total length.
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Dates and versions

hal-02179793 , version 1 (11-07-2019)
hal-02179793 , version 2 (26-04-2021)

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Jean-Jil Duchamps. Fragmentations with self-similar branching speeds. 2021. ⟨hal-02179793v2⟩
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